The shadow cabinet “will not be voting” on the Bill’s second reading in the Commons.

If the majority of Labour MPs abstain, the Bill will certainly pass its first major hurdle with the overwhelming support of Tory MPs, despite opposition from Liberal Democrats.

However, Labour remains determined to prevent the referendum Bill becoming law. The party leadership is convinced it can use other parliamentary tactics to prevent the measure being passed.

As it is a constitutional reform, there will be no limit on debates in the Lords and many amendments are expected to be proposed. There is also no Tory majority in the House of Lords, the Labour source suggested.

Mr Miliband opposes Mr Cameron’s promise to hold a referendum on a renegotiated deal for Britain’s membership of the EU. The Labour leader argues that to promise such a vote four years in advance merely creates uncertainty for businesses that will harm Britain’s interests.

However, other senior figures, including Ed Balls, the Shadow Chancellor, and Jon Cruddas, the party’s policy review chairman, have insisted that Labour must not rule out offering voters a referendum in the next election manifesto.

The Tories immediately accused Labour of denying voters a say over whether Britain should quit the European Union.

Grant Shapps, the Conservative Party chairman, said: “We want to allow the British people to decide our European future with an in-out referendum and we want to turn this commitment into law.

“Ed Miliband has made clear yet again that he is too weak to give his MPs, let alone the public, a say.

“We know there are Labour MPs who want that referendum and we would urge them to ignore their weak leader, back our Bill and let Britain decide.”

Labour sources said they expected a number of eurosceptic MPs on their own side to ignore the party’s orders and support the Bill.

Keith Vaz, the senior Labour MP and former Europe Minister, has been leading a campaign to persuade his party to back a referendum on Britain’s membership of the EU.

Dominic Moffitt, director of the Labour for a Referendum campaign, welcomed the fact that the party "is not seeking to obstruct" the passing of the Bill by ordering MPs to vote against it.

"Since the Labour Party is not whipping for abstention we hope that all Labour MPs who support a referendum will vote for one on the 5th July," he said.